equality

A part of our American Dream is to achieve it’s political ideals…

We hold these truths to be self-evident, that all men are created equal,…

equal treatment, equal protection, equal rights and liberties…

so this reminds me of a heuristic in collaborative filtering (originally text classification for me) When receive rating from users, some users will respond with ratings for more things than other… This tend to create the ability for diligent users to influence the system systematically.

If I only vote for movies with Clint Eastwood, then certainly I could influence a recommendation system that makes recommendations based on lead actor/director.

In fact, if I vote for 100 movies with Cient eastwood in them in one boring afternoon at work. And 100 other people, over the course of a year, come to the system and vote for Sean Connery (born same year, btw).

The influence I have on the system in one pathetic afternoon is going to be same as the collective influence of 100 people over a long period of time (aka all time favorite).

There is of course an easy fix for this. Even most beginners in the field will quickly discover what is commonly known as normalization. My vote for each actor/director is “normalized” by dividing it by the number of votes I made. This means if those 100 people voting for Sean Connery (if they were dedicated fan who would not even consider voting for another actor) would give Sean Connery a total of 100 votes. Where as my 100 votes for Clint Eastwood, would have only given Clint Eastwood 1 additional point.

This is fair!

The first time I ever talked to somebody about this, it wasn’t immediately obvious that a user like me, who spends the afternoon poisoning a recommendation system, should be reweighed. The argument there is, well, if you were such a big fan, and you spend your afternoon boosting your favorite actor’s scores, your dedication means you deserve more voting power.

Hmmmm, well, this is a contrived exmaple, but in other situations this may actually make sense…

Hmm… well, so, this is America, and everybody get’s one vote, and that’s just that. I argued…. yeah, but actually no. We have the electoral college who are aggregated votors that counts for more than you or me.

Hmmm… well, so, here, let’s use (my favorite) naivete. If I am presented with a bunch of scores from two people. Suppose that I have a choice of how much each voting power each of the two people have relative to each other… What should I decide?

well, you can look at the two people and see what race they are, age, gender, etc. all probably will have a major roll in this decision…

well, in theory yes, but in practice, if the two users are visiting from their web browser, you really don’t have that kind of interaction…. and actually, scientifically speaking, the best assumption you can make is the naive assumption. That indeed all men are created equal. In your eyes, you cannot treat them as non-equal and expect, in the large, to have a better result than if you assume they are equal. (hehee… snicker… operative statement here is “better… than…” heeheee)

In reality, the system often have very static biases that make naive assumption more attractive than the theoretic situation in both the average case and worst case. (hmm, say that bad people are always like me and vote 100 or more times. A system that always value people like me more than people who vote less will have worse worst case than the naive-assumption system. (even if it may have same average case performance); and you can further analyze the opposite where people like me are good, and people who vote less are bad, the worst case can equally be worse than naive system; and if we average over all possible worlds, then certainly naive is greatest of them all)

So… it seems there is a level of wisdom in the American political system, that upon careful inspection, has more to it than what it seems to say:

…that all men are create equal…

is not just a statement of belief that “the world is (made) this way”, but more a directive to the government: “Treat them all equal”…

Because this is possibly the best political system we can ever implement.

sigh…

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s